Smooth, Synchronized Robot Motion Achieved with New Algorithm from Taiyuan Researchers
In the rapidly evolving world of industrial automation, precision, speed, and reliability are paramount. As manufacturing lines become more sophisticated, the robots that populate them must execute increasingly complex tasks with flawless coordination. A critical component of this performance is trajectory planning—the process by which a robot’s end-effector is guided from one point in space to another. However, achieving smooth, efficient, and synchronized movement for both the position and the orientation (or attitude) of the end-effector has long been a significant challenge in robotics engineering. Now, a team of researchers from Taiyuan, China, has introduced a groundbreaking algorithm that promises to revolutionize how industrial robots are controlled, offering faster processing, shorter cycle times, and unprecedented motion smoothness.
The new method, developed by Chen Duoduo and Li Lihong of the College of Electrical and Power Engineering at Taiyuan University of Technology, in collaboration with Yuan Gang from the China Coal Technology and Engineering Group’s Taiyuan Research Institute, addresses a fundamental limitation in current robotic control systems. When a robot arm performs a task—such as welding, painting, or assembling components—its end-effector must not only move to the correct location in 3D space but also orient itself at the correct angle. For example, when a robot applies adhesive along a seam, it must follow the path precisely while keeping the nozzle at a constant angle to the surface. This requires two distinct but interdependent motion profiles: one for position and one for attitude.
Traditionally, these two profiles have been planned separately, often using different algorithms, and then stitched together. This approach, while functional, can lead to jerky, inefficient, or even unstable motion. The primary issue lies in the lack of synchronization. If the position trajectory finishes its acceleration phase before the attitude trajectory does, the robot experiences a mismatch in its dynamic behavior, potentially causing vibrations, wear on mechanical components, and reduced product quality. Furthermore, the computational complexity of existing methods, such as the asymmetric S-curve or constrained S-type curves, often makes real-time implementation difficult, especially on embedded control systems with limited processing power.
The research team’s solution, detailed in a recent publication in the Journal of Chongqing University of Technology (Natural Science), is a novel “synchronous acceleration and deceleration algorithm of position and attitude.” At its core, the algorithm introduces a new method for generating smooth motion profiles, called the Quartic Polynomial Acceleration and Deceleration control method based on Function Approximation (QPADFA). Unlike traditional S-curve methods, which rely on piecewise linear or trigonometric functions and require complex conditional logic to handle different motion scenarios (such as very short paths that lack a constant-velocity phase), QPADFA uses a single, continuous polynomial function to model the acceleration profile.
The development of QPADFA began with an analysis of the sine wave acceleration curve, a method known for its smoothness because it produces acceleration profiles without any sudden jumps (or “jerk”). However, the sine function is computationally expensive, requiring significant processing power to calculate trigonometric values in real time. This is a major drawback for industrial robots, which must update their control commands thousands of times per second. To overcome this, the researchers employed a mathematical technique known as the “best square approximation method.” This process involves finding a simpler polynomial function—specifically, a quartic (fourth-degree) polynomial—that closely mimics the behavior of the sine wave but can be computed much more quickly.
The result is a function that retains the desirable smoothness of the sine wave—ensuring that acceleration changes gradually and continuously—while being far more efficient for a robot’s control system to process. In practical terms, this means the robot can plan its motion faster and with less computational overhead. The researchers demonstrated that their QPADFA method reduces program execution time by nearly 50% compared to traditional S-curve methods, a critical advantage for real-time control.
But the innovation does not stop at the motion profile itself. The second, and perhaps more significant, part of the algorithm is the “fully synchronous control strategy” for position and attitude. This is where the true breakthrough lies. Instead of planning the two trajectories independently, the algorithm first calculates the required acceleration, constant-velocity, and deceleration phases for both position and attitude using the QPADFA method. It then compares the durations of these phases. For example, if the attitude trajectory requires 1.5 seconds to accelerate to its target speed, while the position trajectory only needs 1.4 seconds, the algorithm sets 1.5 seconds as the synchronized acceleration time for both.
This ensures that the robot begins accelerating, reaches its peak speed, and begins decelerating for both its position and its orientation at exactly the same moments. The end-effector moves and rotates in perfect harmony. This complete synchronization eliminates the dynamic mismatches that plague traditional methods, leading to smoother, more stable, and more precise motion. It also simplifies the overall control logic, as the system no longer needs to manage two separate, potentially conflicting, timing schedules.
To validate their algorithm, the research team conducted a series of rigorous simulations. In one experiment, they tested the algorithm on a complex multi-path trajectory, where a robot had to move from one point to another, transition through a circular arc, and then proceed to a final destination. This scenario is common in real-world applications, such as when a robot arm moves between workstations. The results showed that the QPADFA method could seamlessly handle the transitions, automatically adjusting its speed and acceleration to meet the geometric constraints of the path, such as the radius of the arc. The velocity and acceleration curves were smooth and continuous, demonstrating the algorithm’s ability to adapt to real-world conditions.
In a second, more direct comparison, the team benchmarked their algorithm against three established methods: the asymmetric S-curve, the constrained S-type curve, and the sine wave acceleration curve. They measured three key performance metrics: the total planned motion time (how long the robot takes to complete the move), the program execution time (how long the control system takes to compute the trajectory), and the smoothness of the resulting motion curve. The results were compelling. Compared to the asymmetric S-curve and the constrained S-type curve, the new algorithm reduced the planned motion time by 5% and the program execution time by nearly 50%. When compared to the sine wave method, which is known for its smoothness but high computational cost, the new algorithm was still 3.2% faster in motion time and 16.4% faster in program execution, while maintaining a comparable level of smoothness.
The implications of this research are far-reaching. In an industry where every millisecond of cycle time can translate into millions of dollars in annual production, a 5% improvement is substantial. Faster motion planning means robots can work more efficiently, increasing the throughput of an entire production line. The reduced computational load allows for the use of less expensive, lower-power control hardware, which can lower the overall cost of robotic systems. Most importantly, the enhanced smoothness of the motion reduces mechanical stress on the robot’s joints and actuators, leading to longer equipment life, fewer maintenance requirements, and higher product quality due to the elimination of vibrations and positioning errors.
The potential applications extend beyond traditional manufacturing. In fields like precision assembly, where robots handle delicate electronic components, or in medical robotics, where stability is critical, this level of synchronized, smooth control is invaluable. The algorithm could also benefit collaborative robots (cobots) that work alongside humans, as smoother, more predictable motion enhances safety.
While the current implementation plans the position and attitude trajectories separately before synchronizing them, the authors acknowledge that the next logical step is to integrate the two into a single, unified planning process. This would further optimize performance and could open the door to even more advanced control strategies. The team’s work represents a significant leap forward in the field of robotic trajectory planning, offering a practical, high-performance solution to a long-standing engineering challenge.
The success of this research is a testament to the growing strength of robotics and automation research in China. The collaboration between a leading academic institution and a major industrial research institute highlights a model of innovation that bridges the gap between theoretical research and practical application. As global manufacturing continues its shift toward smart factories and Industry 4.0, innovations like this will be essential for maintaining competitiveness.
In conclusion, the algorithm developed by Chen Duoduo, Li Lihong, and Yuan Gang offers a powerful new tool for the robotics industry. By combining a computationally efficient motion profile with a robust strategy for full synchronization, they have created a system that is not only faster and smoother but also more practical for real-world deployment. This work sets a new standard for how industrial robots are controlled and paves the way for the next generation of intelligent, high-precision automation.
Chen Duoduo, Li Lihong, Yuan Gang. Synchronous Acceleration and Deceleration Algorithm of Position and Attitude Facing for Industrial Robot. Journal of Chongqing University of Technology (Natural Science), 2021, 35(4): 165-173. doi:10.3969/j.issn.1674-8425(z).2021.04.022